A note on convex renorming and fragmentability |
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Authors: | A K Mirmostafaee |
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Institution: | (1) Department of Mathematics, Damghan University of Sciences, P.O. 36715/364, Damghan, Iran |
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Abstract: | Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach
space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology.
(b) If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) If the Banach
space is weakly locally uniformly rotund, then its weak topology is fragmented by a metric which is stronger than the norm
topology. |
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Keywords: | Fragmentability of Banach spaces topological games renorming of Banach spaces |
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